Calculation of aerodynamic characteristics of a wing profile with discharge of a controllable jet into the external flow

A wing profile of infinite span, whose lower surface is replaced by a system of guide vanes, is placed in a flow of an ideal incompressible fluid. Fluid flows out through the system of guide vanes from the internal cavity of the wing into the external stream, forming a jet in the wake (Fig. 1). The total pressure in the wing cavity and in the jet differs from the total pressure in the outer free stream. The jet boundaries are streamlines extending to infinity, along which there is a discontinuity of the velocity value. The flow of fluid in the internal wing cavity is simulated by a flow caused by a system of suitably located sources, and the system of guide vanes is replaced by discrete vortices.The form of the profile arc is selected so that the fluid flow from the sources in the direction which is nearly opposite the direction of the freestream velocity is restrained by the segment of the contour with high curvature in the vicinity of the leading edge. We consider the flow regime about the profile with an exhausting jet for which the two ends of the arc the points of detachment of the stream and the velocity discontinuity line (profile arc, jet boundary) is a smooth curve, which imposes an additional condition on the magnitude of the circulation. As the model for the study of the flow about a profile with jet blowing we take the arc of a logarithmic spiral.Formulas are obtained for determining the over-all characteristics of the stream forces acting on the profile in the presence of the jet and the total pressure discontinuity. On the basis of the calculations made for a thin wing a qualitative analysis is made for the stream force acting on the profile.The authors wish to thank S. A. Khristianovich for formulating the problem and for his advice.     

Influence of the inlet velocity profiles on the prediction of velocity distribution inside an electrostatic precipitator

The influence of the velocity profile at the inlet boundary on the simulation of air velocity distribution inside an electrostatic precipitator is presented in this study. Measurements and simulations were performed in a duct and an electrostatic precipitator (ESP). A four-hole cobra probe was used for the measurement of velocity distribution. The flow simulation was performed by using the computational fluid dynamics (CFD) code FLUENT. Numerical calculations for the air flow were carried out by solving the Reynolds-averaged Navier–Stokes equations coupled with the realizable k-ε turbulence model equations. Simulations were performed with two different velocity profiles at the inlet boundary – one with a uniform (ideal) velocity profile and the other with a non-uniform (real) velocity profile to demonstrate the effect of velocity inlet boundary condition on the flow simulation results inside an ESP. The real velocity profile was obtained from the velocity measured at different points of the inlet boundary whereas the ideal velocity profile was obtained by calculating the mean value of the measured data. Simulation with the real velocity profile at the inlet boundary was found to predict better the velocity distribution inside the ESP suggesting that an experimentally measured velocity profile could be used as velocity inlet boundary condition for an accurate numerical simulation of the ESP.     

投影光刀法测量碳纤维编织材料烧蚀表面粗糙度

碳纤维编织材料制成的物体，在其表面经过模拟烧饰后，其表面的光反射率很低，本文提出了一种改进的投影光刀法，可以用非接触式的光学测量方法测量其表面的粗糙度分布和细微三维形状，首先在物体表面投影-黑白边界；接收时在CCD上做适度的散焦，因而CCD里可以接收到一灰度渐变的投影界面；选用适当的阈值，可以得到受物体高度调制的投影边界，在后续的数据处理中，采用了边界提取、扫描、线形拟合、图像拼接等技术，可以得到被测区域的细微三维形状数据，进而可以计算出其二维的粗糙度分布。     

基于荧光漂白成像的润滑油膜剪切流速测量

沿润滑油膜厚度方向的剪切流速分布是影响机械部件润滑性能的重要因素.为此,搭建了基于荧光漂白成像的微间隙油膜剪切流速分布测量平台.通过对漂白区域形状演化过程进行图像分析,获得了微米量级间隙中的PB450和PAO6润滑油膜的剪切速度分布.结果表明:在设定测试条件下,厚度为8.5μm的PB450油膜沿膜厚方向的剪切流速近似为典型的线性分布,而相同厚度下的PAO6油膜流速分布表现为非线性塞流,界面附近油膜黏度较中层显著下降.研究还发现,同一滑动速度下,PAO6剪切流速偏离线性分布的程度随膜厚的降低而增加.经过比对分析,试验结果与流体动压润滑条件下的相关数据吻合.     

Effect of generator shape on the structure of internal wave beams in a uniformly stratified fluid

The generation of internal waves by vibrating cylinders with cross sections of various shapes is studied experimentally. It is shown that at large distances from the generator, the profile of the perturbation amplitude of the density gradient can be calculated with satisfactory accuracy using the theory for an equivalent circular cylinder. It is found that at short distances from the generator, its shape has a significant effect on the profile of the generated waves.     

Lattice of plates in an unsteady supersonic flow

The supersonic unsteady flow of a gas past a lattice of thin, slightly curved profiles has been investigated in several studies. The paper [1] is devoted to an evaluation of the effect of wind tunnel walls on the unsteady aerodynamic characteristics of a profile, and [2] investigates the effects of the boundaries of a free jet. These cases are equivalent respectively to the anti-phase and in-phase oscillations of the profiles of an unstaggered grid. In [3] consideration is given to a more general case of gas flow past a profile in a wind tunnel with perforated walls. Flow past a lattice of profiles with stagger is studied in [4], where the magnitude of the stagger angle is limited by the condition that the lattice leading edge is located in the undisturbed stream.In the present paper we present a method of calculation of the unsteady supersonic flow of a gas past a lattice of profiles with arbitrary stagger. As an example the results are presented of the calculation of the aerodynamic forces and moments acting on an oscillating profile in a wind tunnel with solid walls and in a free jet.     

Numerical study on the effect of initial flow velocity on liquid film thickness of accelerated slug flow in a micro tube

Numerical simulation of air–water slug flows accelerated from steady states with different initial velocities in a micro tube is conducted. It is shown that the liquid film formed between the gas bubble and the wall in an accelerated flow is significantly thinner than that in a steady flow at the same instantaneous capillary number. Specifically, the liquid film thickness is kept almost unchanged just after the onset of acceleration, and then gradually increases and eventually converges to that of an accelerated flow from zero initial velocity. Due to the flow acceleration, the Stokes layer is generated from the wall, and the instant velocity profile can be given by superposition of the Stokes layer and the initial parabolic velocity profile of a steady flow. It is found that the velocity profile inside a liquid slug away from the bubble can be well predicted by the analytical solution of a single-phase flow with acceleration. The change of the velocity profile in an accelerated flow changes the balance between the inertia, surface tension and viscous forces around the meniscus region, and thus the resultant liquid film thickness. By introducing the displacement thickness, the existing correlation for liquid film thickness in a steady flow (Han and Shikazono, 2009) is extended so that it can be applied to a flow with acceleration from an arbitrary initial velocity. It is demonstrated that the proposed correlation can predict liquid film thickness at Re < 4600 within the range of ±10% accuracy.     

Computation of the two-dimensional viscous incompressible fluid flow with separation at the nlet edge around a cascade

A complex flow consisting of an outer inviscid stream, a dead-water separation domain, and a boundary layer, which interact strongly, is formed in viscous fluid flows with separation at the streamlined profile with high Re numbers. Different jet and vortex models of separation flow are known for an inviscid fluid; numerical, asymptotic, and integral methods [1–3] are used for a viscous fluid. The plane, stationary, turbulent flow through a turbine cascade by a constant-density fluid without and with separation from the inlet edge of the profile and subsequent attachment of the stream to the profile (a short, slender separation domain) is considered in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 34–44, May–June, 1978.     

Pressure-driven flows of concentrated alumina suspensions depending on dispersion states of particles

The flow developments of 25 vol% alumina suspensions in slit channel were visualized and analyzed depending on the dispersion states. For the coagulated alumina suspension, the shear stress showed an N curve that included a region of stress decrease with an increase in shear rate followed by a monotonic increase. Depending on the region in the stress curve, the flow profile changed from a shear-banded profile to a plug-like flow profile similar to the Newtonian fluid. In addition, it was observed that the transient flow behavior over time at high shear rate in liquid state experienced all of the steady state flow profiles at lower shear rates in solid-liquid transition. During the solid-liquid transition, the flow profile was found to be shear banded, and the pressure profile did not reach a steady state but fluctuated with a characteristic time period. In contrast, the well-dispersed suspension showed only a monotonic increase of shear stress in the range of shear rates we could measure, indicating that the suspension was in liquid state. The flow profile was plug-like, and the pressure was fluctuating without any characteristic time period.     

磨合过程中缸套表面形貌变化的计算机仿真

对磨合过程中缸套表面形貌的变化进行了观测,发现其为原始表面形貌逐渐被新表面形貌取代的过程,最终表面形貌由缸套的磨损和润滑条件决定,建立了模拟磨合过程中缸套表面形貌变化的计算机仿真模型,仿真结果和试验现象吻合较好。     

Reflection of a beam of elastic waves by a periodic surface profile

Reflection of elastic waves from a traction-free solid-air boundary of periodic saw-tooth profile is investigated analytically and experimentally. For an incident plane wave the surface displacements on the profile are computed as the solution of a singular integral equation. The reflected field is subsequently obtained by using an integral representation. Incident beams of finite width are represented by Fourier superpositions of plane waves. The dependence of the reflected signal spectra on the incident beam width is examined closely near the fundamental surface resonance frequency. Experimental spectra which were obtained using two different diameter transducers, are compared to the corresponding theoretical spectra. It is found that the depth of the spectral minima depends on the incident beam width. Both analytical and experimental results exhibit the splitting of an incident beam of elastic waves into two reflected beams. The beam splitting is more pronounced for a narrower incident beam and for frequencies close to a resonance frequency of the profile.     

An external meniscus on a thin ovoidal fiber (the case of full wetting)

A complex shape of an external meniscus formed due to the capillary rise of a liquid along a fiber having the ovoidal profile is considered. Within the framework of the asymptotic approach and under the assumption on the complete wetting of the fiber material by the liquid, an analytical solution of the problem is derived. The particular examples of the meniscus configuration are presented in the cases in which the fiber profile has the shape of an ovoid or an ellipse.     

Elastic contact stiffness and contact resistance for the Weierstrass profile

The Weierstrass series comprises a system of superposed self-affine sine waves that can be used to define a simple idealization of a two-dimensional fractal rough surface profile. The load-compliance relation for the contact of this profile with a rigid plane is here estimated using Westergaard's solution for the contact of a single sine wave with a plane and various approximations concerning the interaction of the different terms in the series. These approximations are compared with a numerical solution for the contact of the profile defined by the first few terms of the series. Once the load-compliance relation is established, the electrical contact resistance can be determined, using an analogy between the conduction and incremental elastic contact problems. The results show that these simple estimates give quite good predictions of the relations between load, compliance and contact resistance. They also confirm that these relations are largely determined by the coarse scale features of the surface profile, in contrast to the predictions of classical asperity model theories.     

Thin shear boundary layers in flow of hot aluminium

The flow of hot aluminium in channels is investigated. The constitutive relation considered for the flow stress is the inverse hyperbolic sine function of the Zener–Hollomon parameter. Analytical solutions for the flow are derived. At high strain rates, an exponential velocity profile close to the channel walls is predicted indicating the existence of a thin shear boundary layer characterized by strong shear. The characteristic length scale for the exponential velocity profile is a function of material parameters in the constitutive relation and the inverse of the local pressure gradient. The analytical prediction of a thin shear boundary layer close to the channel walls for large strain rates is consistent with the observed microstructure in an extruded section.     

Vortex stretching and filaments

This paper presents a new technique to produce controlled stretched vortices. Intense elliptical vortices are created by stretching of an initial vorticity sheet. The initial vorticity comes from a laminar boundary layer flow and the stretching is parallel to the vorticity vectors. This low velocity flow enables direct observation of the formation and destabilization of vortices. Visualizations are combined with quasi-instantaneous measurements of a full velocity profile. The velocity profile is obtained with an ultrasonic pulsed Doppler velocimeter. The evolution of the central diameter of the vortices is related to the stretching. It is observed that destabilization occurs by pairing of two vortices, by hairpin deformation, and by breakdown of vortices into a “coil shape”.     

Precise flow rate measurements of natural gas under high pressure with a laser Doppler velocity profile sensor

This paper reports about the first application of a laser Doppler velocity profile sensor for precise flow rate measurements of natural gas under high pressure. The profile sensor overcomes the limitations of conventional laser Doppler anemometry (LDA) namely the effect of spatial averaging and the effect of fringe spacing variation (virtual turbulence). It uses two superposed, fan-like interference fringe systems to determine the axial position of a tracer particle inside the LDA’s measurement volume. Consequently, a spatial resolution of about 1 μm can be achieved and the effect of virtual turbulence is nearly eliminated. These features predestine the profile sensor for flow rate measurements with high precision. Velocity profile measurements were performed at the German national standard for natural gas, one of the world′s leading test facilities for precision flow rate measurements. As a result, the velocity profile of the nozzle flow could be resolved more precisely than with a conventional LDA. Moreover, the measured turbulence intensity of the core flow was of 0.14% mean value and 0.07% minimum value, which is significantly lower than reference measurements with a conventional LDA. The paper describes the performed measurements, gives a discussion and shows possibilities for improvements. As the main result, the goal of 0.1% flow rate uncertainty seems possible by an application of the profile sensor.     

The effects of inlet conditions and expansion ratio on the onset of flow reversal in swirling flow in a sudden expansion

Experiments are reported in which the minimum swirl intensity required to produce a central recirculation zone in a swirling sudden expansion flow is determined as a function of expansion ratio and inlet conditions. Using a swirl generator which allows for independent variation of velocity profile shape and swirl number, it is shown that an inlet tangential velocity distribution with a large solid body vortex core or an axial velocity profile with a maximum on the axis will lead to a higher critical swirl.     

Prediction of Gear Dynamics Using Fast Fourier Transform of Static Transmission Error*

ABSTRACT

An analytical computer simulation procedure for dynamic modeling of low-contact-ratio spur gear systems is presented. The procedure computes the gear static transmission error and uses a Fast Fourier Transform (FFT) to generate its frequency spectrum at various tooth profile modifications. The dynamic loading response of an unmodified (perfect involut) gear pair is compared with that of gears with profile modifications. Correlations are found between several profile modifications and the resulting dynamic loads. An effective error, obtained from frequency domain anal     

关于Orr—Sommerfeld方程的Chebyshev谱方法的讨论

本文讨论了Ｏｒｒ－Ｓｏｍｍｅｒｅｌｄ方程的各种Ｃｈｅｂｙｓｈｅｖ谱离散方法，数值证明了Ｃｈｅｂｙｓｈｅｖ配置法离散Ｏｒｒ－Ｓｏｍｍｅｒｆｅｌｄ方程没有伪谱，并以此构造了适于任意平面平行速度剖面情形，对时间和时空稳定性模式一致有效的无伪谱的离离散方法，其中，对时空稳定性问题本文给出了一种新的迭代法可以快速有效地求出复频率的鞍点，对平面Ｐｏｉｓｅｕｉｌｌｅ流，Ｂｌａｓｉｕｓ边界层流和Ｇａｕｓｓ模型尾迹     

Numerical and experimental study of free convection above a sinusoidal horizontal plate

A numerical and experimental analysis is performed to study the laminar free convection above a horizontal plate facing upward subjected to an uniform heat flux. The surface of the plate, in contact with the fluid, is described by a sinusoidal profile. The natural convection equations are discretized, using an implicit finite difference technique, based on the finite volume approach. The SIMPLE algorithm assumes the linkage between velocities and pressure fields. The top and the lateral boundaries of the space, where free convection is developing, are determined by using an iterative procedure. The temperature fields of the fluid, over the plate, are visualized by an experimental device, which can realize a simultaneous measurement of the temperature and the position. Qualitative information about the natural convection flow above the plate is obtained by using a laser tomography technique. The numerical results show that the flow and the heat transfer are strongly affected by the amplitude, the period of the sinusoidal profile and the type of fluid. Comparisons between numerical and experimental results show a good qualitative agreement.